Collision Avoidance for Underactuated Marine Vehicles Using the Constant Avoidance Angle Algorithm

Abstract

Avoiding collisions is a crucial ability for unmanned vehicles. In this paper, we present the constant avoidance angle algorithm, a reactive method for collision avoidance. It can be used to avoid both static and moving obstacles by making the vehicle keep an avoidance angle between itself and the obstacle edge. Unlike many other algorithms, it requires neither knowledge of the complete obstacle shape, nor that the vehicle follows a desired speed trajectory. Rather, safe vehicle headings are provided at the current vehicle speed. Thus, the speed can be used as an input to the algorithm, which provides flexibility and makes the approach suitable for a wide range of vehicles, including vehicles with a limited speed envelope or high acceleration cost. We demonstrate this by applying the algorithm to a marine vehicle described by a full kinematic and dynamic model in three degrees of freedom. We specifically consider vehicles with underactuated sway dynamics, where the vehicle velocity contains a component which cannot be directly controlled. Such dynamics can be highly detrimental to the performance of collision avoidance algorithms, and need to be included in the design and analysis of control systems for such vehicles. In this paper, we compensate for the underactuation by including these dynamics in the underlying analysis and control design. We provide a mathematical analysis of sparse obstacle scenarios, where we derive conditions under which safe avoidance is guaranteed, even for underactuated vehicles. We furthermore show how the modular nature of the algorithm enables it to be combined both with a target reaching and a path following guidance law. Finally, we validate the results both through numerical simulations, and through fullscale experiments aboard the R/V Gunnerus.

A 3D reactive collision avoidance algorithm for underactuated underwater vehicles

“…To limit the yaw and pitch rate, and hence the induced sway and heave motions, the proportional effect is saturated (Wiig et al, 2019):…”

“…A new constant avoidance angle algorithm is proposed in Wiig, Pettersen, and Krogstad (2019). This algorithm provides a safe heading for a given desired forward (surge) speed trajectory.…”

“…In this paper, we extend the constant avoidance angle algorithm in Wiig et al (2019) to 3D. In short, the algorithm we propose creates a cone of velocity directions which are safe at the current speed, and the full flexibility offered by operating in 3D space is utilized when choosing among them.…”

“…presented in Wiig et al (2019), an extension which is nontrivial due to the presence of composite rotations in 3D. Conditions are given under which the Flow frame controller is feasible, and under which obstacle avoidance is still guaranteed, despite the underactuation.…”

“…We show how this component is inherently accounted for by the algorithm, and provide conditions under which the avoidance maneuver is still provably safe. This obstacle velocity compensation is an extension of the technique used in 2D in Wiig et al (2019); if both the vehicle and the obstacle moves in the same horizontal plane without pitching they are equivalent. By extending the technique to 3D, we are able to consider the obstacle velocity also when utilizing the added maneuvering flexibility.…”